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Astron. Astrophys. 329, 799-808 (1998)

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5. Results for n and Q

Figs. 8 and 9 show the strong anti-correlation between n and Q. This has been observed and discussed by many authors (e.g. Smoot et al. 1992, Seljak & Bertschinger 1993, Lineweaver 1994). This anti-correlation has a simple explanation. In the [FORMULA] plot, any increase of the slope lowers the y-intercept (at [FORMULA]) and any decrease of the slope raises the y-intercept. The anti-correlation is thus inherent with the use of the amplitude at [FORMULA] as the normalization.

[FIGURE] Fig. 8. Likelihood contours in the [FORMULA] plane for [FORMULA] and [FORMULA]. Result [FORMULA] and [FORMULA], or at the 95% CL, [FORMULA] and [FORMULA] K. This standard model has been looked at by several other workers who obtain similar results (see Sect. 5).

[FIGURE] Fig. 9. Likelihood contours in the [FORMULA] plane for h free and [FORMULA] free. [FORMULA], [FORMULA] K. The minimum is at [FORMULA], [FORMULA], and [FORMULA].

The increase of the size of the error bars on n and Q as h and [FORMULA] are conditioned on and then marginalized can be seen by comparing Figs. 8 and 9. Our n and Q results are [FORMULA] and [FORMULA] K from Fig. 9 where both h and [FORMULA] have been marginalized. Conditioning on [FORMULA], we get [FORMULA] K (see also Fig. 6).

The four year COBE-DMR constraints on the amplitude and slope of the power spectrum at large angular scales are [FORMULA] and [FORMULA] K, and conditioning on [FORMULA], [FORMULA] K (Bennett et al. 1996). These DMR results are in the context of [FORMULA], [FORMULA] CDM models and they need to be corrected due to the mildly model-dependent extended tails of the Doppler peak which reach even into the low- [FORMULA] region. After the correction, the DMR result becomes [FORMULA] and [FORMULA] K. Thus our results from a combination of recent CMB measurements in the context of critical density universes agrees well with the DMR-only result and reduces the error bars on both n and Q.

For the standard CDM model of Fig. 8 ([FORMULA], [FORMULA] and [FORMULA]), we obtain [FORMULA] CL) and [FORMULA] K (95% CL). Using similar methods and a similar data set, several authors have reported similar results. de Bernardis et al. (1997) find [FORMULA] CL). White et al. (1996) find [FORMULA] ([FORMULA] CL). Hancock et al. (1997) find [FORMULA] ([FORMULA] CL). The variations of these standard model n determinations are probably due to slightly different data sets, different treatments of the Saskatoon calibration and the details of the [FORMULA] calculation.

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997